Calculating the hardenability of steels

In the last article, I discussed the concept of hardenability of steels. Hardenability is not to be confused with the achievable hardness of an alloy, but rather how deeply the alloy hardens. Various alloying elements such as chromium, nickel, and molybdenum are added depending on the steel alloy used. It is the carbon content that provides the ultimate hardness. It is the alloying elements that govern how deeply the alloy will harden. The purpose of this article is to quantify these effects.

Introduction

Fundamentally, hardenability is a measure of how alloying elements and prior austenite grain size shift the transformation curve from the time-temperature-transformation diagram to longer times. In other words, alloying elements and grain size shift the nose or knee of the C-curve to slower times, delaying the transformation of austenite to pearlite and bainite. This allows the austenite to transform to martensite at lower cooling rates, and at a greater depth below the surface for a similar quench rate.

There are several different methods of determining hardenability of a steel. These include both calculation and empirical methods. In this article the focus will be on calculating the hardenability of steels. Another article will discuss empirical methods of determining hardenability.

Critical Cooling Rate

The earliest method of determining hardenability was based on examining the critical cooling rate from continuous-cooling-transformation diagrams (CCT curves) [1] [2]. This is the minimum cooling rate needed to prevent the transformation of bainite or pearlite, or the slowest cooling rate needed to produce 100 percent martensite [3]. The minimum cooling rate can be obtained from the CCT diagram using (Equation 1) [4]:

where T_A is the austenitizing temperature (°C), T_N is the temperature at the nose or knee of the CCT diagram (°C), and I_N (s) is the incubation time, or the corresponding time on the CCT curve. If there are two knees, such as in SAE 4340, use the lower knee as T_N, and its corresponding time for I_N.

Alternatively, Zeng and Xu [5] developed a regression equation to obtain the minimal critical cooling rate (V_M), and a 100 percent martensitic structure (Equation 2):

In this equation, the concentrations of the various alloying elements are shown in weight percent. This equation does not consider the effects of grain size, and assumes that modern steels have a smaller, more consistent prior austenite grain size. While this is generally true for most steels produced by Japan, Germany, and the United States, it is not necessarily true for all steel-making countries. It is always good to verify the grain size.

By comparing the critical cooling rate, the steel with the lowest critical cooling rate, V_M, has the greater hardenability.

Carbon Equivalence

A method, based on the chemical composition of the steel, is the concept of carbon equivalent, or C_eq. This method is really two-fold. First, it is an approximate measure of hardenability when compared to another steel, and secondly, it provides an estimation regarding the sensitivity to quench cracking. There are many different equations, but one that is commonly used is (Equation 3) [6]:

In the above equations, the concentrations are given in weight percent. The greater the carbon equivalent, C_eq, is, the greater the hardenability. This method ignores the effects of grain size. This method is somewhat alloy dependent, and should not be treated as exact for all steels, due to the difference in the TTT and CCT diagrams.

Calculation of Ideal Diameter, D_I

This method is based on the work of M. A. Grossman [7] [8]. In his work, D_I is the diameter that would give 50 percent martensite at the center under an ideal quench, meaning an infinite quench rate. This is a quench rate where the surface of the steel is cooled to the temperature of the quenchant instantaneously. In other words, this is not a property of the quenchant, but the steel itself. The cooling rate at the center of the bar is only dependent on the thermal diffusivity of the steel. Computationally, it is also much easier to calculate.

Using the 50 percent martensite criteria from Grossman [8], the hardenability can be calculated multiplying a reference diameter (D_C) that is only a function of carbon content and grain size, by concentration dependent hardenability multiplying factors (Equation 4):

where D_C is the carbon factor, F_i are the alloy multipliers, and F_g is the grain-size factor. In other words, it is (Equation 5) [9] [10]:

The factors for individual elements can be obtained from ASTM A255 [11] or Table 1.

From D_I, extrapolations can be accomplished using quench severity, to estimate the hardness of real parts using real quenchants.

Conclusions

In this article, the calculation of hardenability was discussed from different aspects — first, estimating hardenability from the CCT diagram; secondly, determining the hardenability from the carbon equivalent; and lastly, the traditional method established by Grossman, and embodied in ASTM A 255.

In the next article, I will discuss empirical methods of determining hardenability. Should you have any questions or comments regarding this article, or suggestions for additional articles, please contact the editor or the author. 

References

1. P. Wever and A. Rose, “On the Question of Heat Treatment of Steels on the Basis of Time-Temperature-Transformation Diagrams,” Stahl und Eisen, vol. 74, no. 12, pp. 749-760, 1954.
2. L. C. Canale, L. Albano, G. E. Totten and L. Meekisho, “Hardenability of Steel,” in Comprehensive Materials Processing, vol. 12, G. Krauss, Ed., Elsevier Ltd., 2014, pp. 39-97.
3. G. Krauss, Steels — Processing, Structure, and Performance, 2nd ed., Metals Park, OH: ASM International, 2015.
4. G. Totten, C. Bates and N. Clinton, Eds., Handbook of Quenching and Quenchants, Metals Park, OH: ASM International, 1993.
5. Q. Y. Zeng and K. Y. Xu, “Predicting the Hardenability of Steel Using the Critical Cooling Rate,” Me´moires et E´tudes Scientifiques Revue de Me´tallurgie, no. February, pp. 105-110, 1988.
6. T. Kasuya and Y. Hashiba, “Carbon Equivalent to Assess Hardenability of Steel and Prediction of HAZ Hardness Distribution,” Nippon Steel, 2007.
7. M. A. Grossman and M. Asimov, “Hardenability and Quenching,” Iron Age, vol. 145, no. 17, pp. 25-29, 1940.
8. M. A. Grossman, “Hardenability Calculated from Chemical Composition,” Metals Technology, pp. 1-29, June 1942.
9. D. V. Doane and J. S. Kirkaldy, Eds., Hardenability Concepts with Applications to Steel, Warrendale, PA: The Metallurgical Society of AIME, 1978.
10. E. Just, “New Formulas for Calculating Hardenability Curves,” Metals Progress, no. November, pp. 87-88, 1969.
11. ASTM, “Standard Test Methods for Determining Hardenability of Steel,” ASTM International, West Conshocken, PA.